Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations
Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations
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发表时间：
2020-06
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通讯作者：
Alexander Ritchie;Robert A. Vandermeulen;C. Scott
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作者：
Alexander Ritchie;Robert A. Vandermeulen;C. Scott
最近的研究已经建立了有限混合模型从分组观测中可识别的充分条件。这些条件允许混合成分是非参数的，并且具有大量（甚至全部）重叠。这项工作提出了一种算法，一致地估计任何可识别的混合模型从分组的意见。我们的分析利用了一个甲骨文不等式的加权核密度估计的分布组，连同一个一般的结果表明，一致的估计组的分布意味着一致的估计的混合成分。一个实际的实施提供了成对的观察，该方法优于现有的方法，特别是当混合成分重叠显着。
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap. This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations. Our analysis leverages an oracle inequality for weighted kernel density estimators of the distribution on groups, together with a general result showing that consistent estimation of the distribution on groups implies consistent estimation of mixture components. A practical implementation is provided for paired observations, and the approach is shown to outperform existing methods, especially when mixture components overlap significantly.